q.16 a function of two variable varies directly with x and inversely with y. determine function when x = 5 and y = 3 given that, for x = 0 and y = 1 f = 15 and for x = 1 and y = 15 f = 2

The problem states that a function \( f(x, y) \) varies directly with \( x \) and inversely with \( y \). This implies that the function can be written as:

\[
f(x, y) = \frac{k \cdot x}{y}
\]
where \( k \) is a constant to be determined.

We are given the following conditions:

1. When \( x = 0 \) and \( y = 1 \), \( f = 15 \).
   \[
   f(0, 1) = \frac{k \cdot 0}{1} = 15
   \]
   This simplifies to:
   \[
   0 = 15
   \]
   This is a contradiction, so it seems there is some issue with the information. However, we can proceed with the other given condition to determine the function.

2. When \( x = 1 \) and \( y = 15 \), \( f = 2 \).
   \[
   f(1, 15) = \frac{k \cdot 1}{15} = 2
   \]
   Solving for \( k \):
   \[
   \frac{k}{15} = 2 \quad \Rightarrow \quad k = 2 \times 15 = 30
   \]

Thus, the function is:

\[
f(x, y) = \frac{30 \cdot x}{y}
\]

### Verification
Let's verify this with the condition when \( x = 5 \) and \( y = 3 \):

\[
f(5, 3) = \frac{30 \cdot 5}{3} = \frac{150}{3} = 50
\]

So, the function works under this condition.

If the first condition still seems incorrect, it may need to be revised or removed from consideration. Would you like further clarifications or help with this?

Here are 5 related questions:
1. How does variation affect a function’s form?
2. Can direct and inverse variation happen simultaneously in real-world problems?
3. How can we solve similar problems with three or more variables?
4. What are the common types of mathematical variations used in functions?
5. How does dimensional analysis help in interpreting function variations?

**Tip:** When solving problems with direct and inverse variations, carefully identify constants and use the given conditions to solve for them.

Learn how to determine a function of two variables that varies directly with x and inversely with y. This problem involves direct and inverse variation concepts, including solving for constants using algebraic equations. Given conditions include x = 5, y = 3, f = 15 for x = 0, and f = 2 for x = 1.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation